In this paper we focus on the demonstration and application teaching of Lusin Theorem based on PBL and CBT. In teaching of the course, by inventing problems, offering conjectures and proving them, we develop the Lusin theorem and present examples for applying Lusin theorem. We develop a new teaching mode of problem-driven-conjecture-theorem-cases of applying theorem, so that students can better understand the origin, conclusion and extension of Lusin theorem and grasp the idea, method and skill of applying Lusin theorem.